Book 4 Capital Modelling

Question 1

Give examples of applications of the output that could demonstrate that a capital model satisfies a ‘use test’ - Applications of Capital modelling output

Answer 1

Setting regulatory capital.
Reinsurance: optimising the purchase of reinsurance by testing alternative
structures.
Assessing profitability of new lines of business/existing business is evaluated using the internal model
Projecting future profit and loss accounts enabling testing of actual experience compared to expectations.
Informing, managing or reviewing risk appetite
Reviewing investment portfolio and testing alternative strategies.
Regular and evidenced Board review of internal model output.
Capital allocation to individual underwriting units.
Aggregation monitoring/ assessing catastrophe exposures.
Designing and monitoring risk management systems: identifying key risks and assessing the impact of mitigation
Setting bonuses/performance related salary for underwriters/management
Pricing: assessing return on capital for pricing and performance measurement
Reserving: quantifying the uncertainty in claims reserves
Planning: assessing different plans in terms of their risks, not just expected profits
Strategy: assessing the risks and diversification benefits of new strategies
Any other reasonable application

Question 2

Outline the methods the insurer could use to allow for diversification between reserving and underwriting risk.

Answer 2

Allow for different types of correlations, eg by Class of business / year / claim size.
Introduce implicit dependencies:  eg using explicit formula  measure the correlation of the results, to help validate the model  specific scenarios may also include implicit correlations.

Use explicit correlation factors, in a correlation matrix:  assumes constant correlation across all points on the distributions  whereas we’d expect higher correlation in the tails.

Use copulas:  provide greater flexibility  useful for specifying multiple dependencies  eg Gumbel copula is non-symmetric and gives a strong tail correlation.

Deterministic allowance for diversification:
 sum the variances of the distributions for reserving risk and underwriting risk
 but unlikely to be appropriate, since a stochastic model is being used.

Question 3

Appropriate considerations that a small GI company who has entered run off should make in setting its investment policy, suggesting appropriate investment types

Answer 3

Invest assets to match amount / nature / term / volatility and currency of liabilities and thereafter maximise return, subject to risk appetite. Use an asset liability model to help choose matching assets.
Characteristics of insurer:
 real liabilities, eg price inflation for PD claims, court award inflation for liability claims
 short-tailed PD claims, medium-/ long-tailed liability claims, depending on business written
 volatile liabilities due to individual large losses / accumulations / catastrophes
 but volatility reduces once business is fully earned  probably domestic currency for a small company  expenses becoming more significant as the business runs-off  probably low solvency because company is in run-off  hence, little investment freedom  if assets and liabilities are valued on consistent basis, than a rise in liabilities would be offset by a rise in asset values, hence mismatching might be possible
 regulation affects ability to mismatch  premium income will continue only until all business is earned (ie in less than a year)
 hence, higher than normal liquidity risk and lower risk appetite  small company, so little expertise.

Investment strategy should match characteristics of liabilities:
 amount - hold sufficient assets to pay liabilities with confidence, eg 99.5% percentile
 term - a mixture of short / medium / long-term bonds
 nature - real assets to match inflation risk, eg index-linked bonds (if available / reasonably priced)
 volatility - cash and short-term government bonds to provide liquidity
 choose lower duration than term of liabilities to reduce liquidity risk further
 catastrophe bonds and post-loss funding to match catastrophe risk
 currency - probably domestic assets
 expenses - increasing need for cash / liquidity as business runs off
 low risk appetite - secure, stable assets
 avoid equities and property, even for free reserves (despite matching term and nature)
 but consider equity if exposed to latent claims  extra liquidity needed to enter commutation agreement quickly  income yielding rather than capital growth assets  highly-rated corporate bonds to diversify / increase return (but depends on risk appetite)
 comply with regulation (eg shorter-dated, conventional bonds may be required for a company in run-off)
 changes to existing asset mix will incur costs and crystallise investment losses
 consider time-frame required for new strategy  reinsurance programme will reduce need for liquidity  non-investible assets increase need for liquidity  credit facilities reduce the need for liquidity  consider tax treatment of assets / insurer.

Recommendation:
 conventional government stock / highly rated corporate bonds, of matching term (or shorter), high coupon rate, and some index-linked stock
 some cash for liquidity  avoid equities or property.

Question 4

Variables modelled in an economic scenario generator

Answer 4

 inflation, eg wage inflation, price inflation, etc interest rates
 exchange rates 
 unemployment rates 
 GDP 
 equity returns, eg share indices 
 dividend yields 
 property returns
 bond yields 
 yield curve shifts 
 credit spread shifts 
 credit default rates 
 information on derivative contracts, eg option price volatilities

Question 5

Suggest interdependencies between assets and liabilities that should be considered for representation within the ALM framework.

Answer 5

A catastrophe will lead to:  very poor claims experience and a fall in asset values  increased credit spreads and higher risks of reinsurer defaults.
Inflationary increases will lead to:  higher claims and expenses  an increase in the value of real assets  a fall in the value of fixed interest assets.
Higher interest rates may lead to:  worsening claims experience, eg on credit insurance  lower discounted value of assets.
If equity markets fall, there could be:  increased defaults from reinsurers  higher claims rates due to fraud of distressed companies.
A fall in property values would increase MIG (Middle Income Group) claims. Tax changes could lead to higher claims and lower returns on assets.
The collapse of one company could lead to increased D&O claims and the default of bonds held by the insurer.
Operational risks could mean that assets are overvalued and liabilities are undervalued.
A stronger overseas currency will increase overseas claims and asset values, once those values have been repatriated.
Regulatory changes could affect asset valuations and liability valuations.

Question 6

Operational controls that could be put in place around the assumptions that are used in ALM model

Answer 6

 ensure that model / parameter risk is included in the company’s risk register
 maintain assumptions in a central location to ensure consistency across the business
 maintain accurate and detailed data  cross-check data with the data used in the previous review  check assumptions for reasonableness  obtain opinions from claims handlers / underwriters, etc  check validity of model output  perform sensitivity tests to understand the key drivers of the results  obtain independent reviews of model / assumptions / output  check compliance with regulation / professional guidance  sign off methodology / assumptions by designated people  introduce a formal policy surrounding model changes  document the rationale for choosing assumptions  communicate the uncertainty surrounding the assumptions  review the appropriateness of assumptions at regular intervals

Question 7

A Lloyd’s syndicate has been advised that it would require a higher level of capital to support its business plan for the next underwriting year. Describe options available to the syndicate.

Answer 7

Action(s) depend on the size of the shortfall. A combination of actions is likely to be needed. Reduce the volume of business written  but still need to cover fixed costs.
Write less capitally-intensive business, eg lower layer RI, smaller risks, regions not exposed to catastrophes, property rather than liability. Increase diversification, eg write more classes, or diversify within a class.
However, the diversification already appears to be significant, and will only affect underwriting risk, which is relatively small. Increase business volumes, in the hope of additional profits. Purchase more RI, to reduce insurance risk and volatility.
Arrange a commutation / loss portfolio transfer  but can be time consuming and may not improve the capital position if favourable terms are not obtained.
Reduce market risk by investing in lower risk assets, or exiting classes exposed to currency risk.

Reduce credit risk capital by using more highly-rated reinsurers, requiring reinsurers to post collateral, and controlling broker balances.
Reduce operational risk by implementing controls. Reduce liquidity risk by matching liabilities or increasing premium income.
Alleviate Lloyd’s concerns by providing additional information, improving the capital model, or engaging an independent actuary.
Further capital could be obtained from Names / the parent company / financial reinsurance arrangements / other finance provider.

Question 8

Give examples of requirements that a regulator may set regarding validation of a capital model.

Answer 8

 methods that should be used  specific validation tests to be carried out  frequency of validation
 compare results against the standard formula  external validation and/or peer review  undertake regular reviews of company’s validation approach  ensure any previous issues identified have been suitably addressed  specific documentation  documentation may need to be provided to the regulator  public disclosure requirements 
governance requirements
 require those responsible for validation to have certain experience and/or qualifications
 requirements regarding data inputs and external models used

Question 9

Describe methods of validating a capital model

Answer 9

1. Stress testing quantifies the effect of varying single parameter - Can be used to identify/quantify impact of different stress scenarios on an insurer’s expected financial position. Tests can be deterministic or based on probability distributions. Can focus on understanding specific risks in isolation
2. Scenario testing quantifies the effect of a change in a combination of parameters - Useful for testing the combined effect of a number of risks (and mitigating
   actions).
3. Sensitivity analysis is the process of testing how results change following a small change in one of the assumptions. The purpose is to identify the more sensitive assumptions in the model. Not possible to test all assumptions in complex model so consider changing
   block of assumptions (e.g. loss ratio variance) by a fixed amount or look at largest classes.
4. Back testing is the process of comparing actual experience with model output. The purpose is to test how well the model predicted the outcomes that actually
   occurred. Assessment will need to be made as to whether any deviations are random or are a consequence of limitations in the model.
5. Model documentation is essential for providing a verifiable audit trail in the development and operation of the model. Documentation should cover rationale for selecting assumptions and the particular risk issues considered.
6. Peer review should be undertaken by someone not involved in the day to day capital modelling…
   …this can be done internally or using an external specialist.
7. Market benchmarking enables comparison of key assumptions and results with those of similar companies.
   Benchmarks may be available from regulators, market bodies or actuarial consultants.
8. Analysis of change compares key inputs and outputs of the latest model to theprevious version of the model..
   ..and provides a mapping of the key drivers of any changes.
   Reverse stress testing is the process of considering the scenarios that could
   lead to failure of the overall business model
   The purpose is to test that the overall model does capture major exposures and
   key business risks
   P&L attribution is the process of reviewing outcomes from the prior accident
   year and testing them against the modelled parameters
   The purpose is to create a cycle of feedback that drives a process of
   continuous refinement and to ensure that there are no material sources of
   volatility not represented within the model
   Any other validation technique
   ..and appropriate explanation of technique.

Question 10

Outline methods of allowing for diversification in a capital model.

Answer 10

1. Linking assumptions.
   If two assumptions are linked by a formula this introduces an implicit correlation between them. e.g. inflation
2. Explicit correlation between distributions.
   Apply correlation factors/matrices between parameters in a model.
3. Copulas
   Mathematical relationship between individual distributions of random variables and
   joint distribution of their variables.
   Allows more complex/flexible non-symmetric dependencies.
   Many different copula structures based on different probability distributions. e.g. Gumbel Copula which gives stronger tail dependency.
4. Deterministic allowance for diversification.
   Use standard methodology for summing variances of distributions.
   Can use correlation matrix to extend to more than two risks.
5. Implicit correlations.
   These can arise as a result of a single event (e.g. earthquake) impacting a number of different risks.

Question 11

List typical investment policy objectives for a general insurer.

Answer 11

The prime objective regarding the investment of the assets supporting these liabilities is to maximise investment return, subject to meeting all contractual obligations whilst ensuring the risk against not receiving the return is within the company’s tolerance.
The implication for asset choice is that the characteristics of the assets should match those of the liabilities (claims and expenses); for example in relation to:  term of the liabilities  amount of the liabilities  nature of the liabilities  currency of the liabilities.

Question 12

Outline the sources of potential volatility that should be considered when parameterising the underwriting risk component of a capital model.

Answer 12

Risks relating to business yet to be written / earned.
Normal statistical variance in outcomes / process error
. . . Large claim frequency
. . . Large claim severity
. . . Frequency of smaller claims
. . . Catastrophe or other accumulation outcomes
More systemic variance in outcomes / parameter error
. . . error in starting loss ratio assumptions
. . . e.g. mispricing risk
. . . anti-selection risks
. . . misjudgement of claims environment
. . . court awards
…..inflation
….. legislation
. . . poor coverholder / underwriter management (may be more operational
risk)
. . . poor aggregation management of CAT exposures
…..mix of business misguessed
Correlation between classes
Correlation between attritional / Large / Cat
Expenses and Profit
Underwriting Cycle
Economy
New Latent Claims
Reinsurance considerations (not credit risk)

Question 13

Why is poisson distribution unsuitable for following class of business: EL, Professional indemnity, Property risk excess of loss, Terrorism

Answer 13

1. Employers’ liability
   Large losses are unlikely to be independent since:  a policy covering a single employer could be subject to a number of large losses from the same incident
    employers in similar industries could be subject to large losses at the same time
    employers in similar industries could be subject to a new type of latent claim
    the claims will be subject to similar influences from the external environment.
2. Professional indemnity
   Large losses are unlikely to be independent since:  a policy covering a single company could be subject to a number of large losses from the same error
    the coverage is normally written on a claims-made basis meaning that policies could be subject to class actions
    the state of the economy is a key driver of claims.
3. Property risk excess of loss:
   Multiple large losses from the same property at the same time are unlikely.
   Geographical accumulations may cause large losses from multiple properties at the same time.
   Most of these are likely to be caused by catastrophe events, which would be covered by catastrophe XL reinsurance.
   There could be some geographical accumulations from smaller non-catastrophic events.
   Large losses in this class are more likely to be independent than for the other classes considered and therefore the Poisson assumption may not be unreasonable.
   The economy is not a big driver for property risk excess of loss as additional claims unlikely to reach excess layers.

4.Terrorism
Large losses are unlikely to be independent since:  attacks often occur in clusters at the same time  attacks are influenced by the political environment  claims are likely to be subject to geographical accumulations.

Question 14

Outline how a general insurance company might typically allow for operational risk in its capital model.

Answer 14

Most common method is to produce operational risk scenarios… [½]
…material operational risks (within risk register) discussed during a
brainstorming session to directly derive an operational risk capital charge at
particular confidence levels. [1]
Stochastic techniques used infrequently as firms rarely have enough history of
extreme operational failures in order to utilise stochastic methods…. [½]
…Instead judgements made about degree of loss that each risk may give rise
to, the type of event that may cause the loss and the frequency of such a loss
occurring. [1]
…In addition, we may consider each loss gross and net of any mitigating
controls. [½]
Broad-brush measures (setting an operational risk capital charge to be a
defined percentage of other risk charges) are not generally accepted… [½]
…as this does not demonstrate a thorough assessment of operational risk. [½]

Question 15

Describe six metrics which could be produced from the capital model’s output to assist in optimise its quota share and excess of loss programmes for business to be written over the next year

Answer 15

1. Loss ratio Defined as:
   expected incurred claims/expected earned premiums
   Can be considered on either a gross, net or ceded basis.
   The net and ceded loss ratios should be calculated allowing for reinstatement premiums. Gives an indication of how much profit the insurer is ceding to the reinsurer. Capital requirements
   By comparing the capital required under different reinsurance structures, the insurer can identify the arrangement which minimises its requirements.
   Can also compare this with its capital requirements in the absence of any reinsurance.
2. Return on Capital Defined as: post-tax profit / free reserves.
   Can be considered on either a gross, net or ceded basis.
   The gross return on capital will give an indication of the returns achievable in the absence of reinsurance.
   The net return on capital identifies the return achievable under the programme being considered.
   Comparing the two will indicate how much purchasing reinsurance has reduced the return achievable.
   When considering the ceded return on capital, a lower value is better as this indicates that less profit is being ceded relative to the capital saved.
   It gives an indication of the capital efficiency of the proposed reinsurance arrangement.
   By contrast the insurer will be looking to increase its gross and net return on capital.
   The expected return on capital can be calculated separately for each individual programme.
3. Reinsurance exhaustion
   Investigate the expected return periods of any exhaustion to the excess of loss reinsurance layers. Will enable the insurer to fine tune its reinsurance programme.
4. Attachment points
   Investigate the expected return periods at which each layer of excess of loss reinsurance is utilised. Enables the insurer to adjust the limits and attachment points of its reinsurance layers.
5. Combined ratio: Defined as: claims ratio + expense ratio. Can be considered on either a gross, net or ceded basis. On a net (and ceded basis) this would allow for any expenses of purchasing reinsurance, brokerage and reinsurance commission received.
   The ceded combined ratio can give an indication of the margin being achieved by the reinsurer, which can be used in negotiations.
6. Quota share profit commission
   Calculate the expected amount of profit commission received from the quota share reinsurer, or the expected frequency with which profit commission is received.Ensures all factors relating to the quota share reinsurance are taken into consideration.
7. Reinstatement costs
   Could look at the expected cost of reinstatement premiums or the expected frequency with which reinstatement premiums are payable. May be able to use this information to negotiate more favourable terms.
8. Capacity limits
   Could investigate its net exposure to any catastrophes after allowing for the proposed reinsurance arrangement, to help with its exposure management.
9. Interval metrics
   All of the metrics considered can be calculated for each future time period and comparisons can be made over time.
   May help the insurer understand the impact on both the SCR and the ultimate SCR. (iii) Possible problems

Question 16

Ways to parametrise and model operational risks

Answer 16

 unlikely to be sufficient volume of operational events to allow detailed statistical modelling
 companies likely to respond to past operational events by improving processes, making past datasets invalid
 benchmark data may be of some use but nature of operations tends to differ significantly between companies
 many operational events are hard to separate from events in other risk categories
 a broadbrush approach is unlikely to be appropriate
 typical parameterisation approach: – is subjective – ideally involves input from other stakeholders – builds on other processes, eg risk register & controls – considers risk mitigation impacts of various controls – uses external expertise where appropriate
 generally use a scenario-based approach …  … or sets of similar scenarios …  … with estimates of frequency and severity …  … or severity at various return periods …  … considering correlation between events  scenario-based approach can be converted into a distribution of outcomes to input to a stochastic model …
 … considering correlation with other risk categories  limited data to determine the parameters stochastically but can model using simulations of operational risk losses …
 … usually model as frequency / severity …  … can model using probability distributions for combined risks or individual risks

Question 17

How to allocate capital by class of business and product for performance measurement purposes

Answer 17

Read more in X Series Solution X5.2 Page 1312
Methods:
Allocate using the same or different risk measure used in assessing the capital requirement. [1]
Solvency capital requirement may be based on a target percentile in the tail of the underlying aggregate loss distribution… [½]
but may allocate the diversified capital down to individual classes of business or products with reference to a lower percentile… [½]
or with reference to various percentile-defined layers… [½]
to prevent over-allocation to catastrophe-type business. [½]
Marginal capital method (a “last in” method)… [1]
…allocate the capital with reference to the marginal capital requirements of each segment. [½]
The Shapley method… [1]
…an extension to the marginal capital method based on game theory. [½]
…Capital is allocated with reference to an average of the marginal capital requirements, assuming that the class under consideration is added to the overall portfolio first, second, third and so on. [½]
…Shapley method can be unworkable in practice as the number of scenarios that needs to be run is the factorial of the number of classes… [½]
…however, it can be used for a small number of classes. [½]
Marks available for other methods (e.g. proportional method) with appropriate explanation / examples (1 per method / example) [3]
General Issues
Consider the use to which the results will be put… [½]
…and desirable properties of the results, such as stability over time. [½]
Not necessarily one method that is best suited in all cases. [1]
Typically, compare the results from several methods of allocation and use judgement when recommending or setting the final allocation. [1]
As the capital allocated includes a diversification credit, the diversification assumption for each class of business in this case would be implicit. [½]
Important to distinguish between Total capital, Economic capital and Excess capital. [1]
…We will normally allocate economic capital to each class of business in proportion to its contribution to the risk metric on a standalone basis. [½]
..We may allocate the excess capital between classes of business pro rata to its risk-based capital or certain components of it, depending upon the purpose of the exercise.

Question 18

External influences on investment strategy

Answer 18

 tax treatment of different investments  ethical considerations  statutory valuation requirements  regulatory requirements, including solvency requirements
 rating agency requirements / views  competition – strategy followed by other insurers  relative expected return  riskiness of different investments  economic outlook  risk appetite of investors  inflation rates
 assets available for purchase

Question 19

List the characteristics of a good model

Answer 19

Fit for purpose [½]
Adequately documented [½]
Follows professional guidelines [½]
Not overly complex [½]
Flexible [½]
Understandable by managers [½]
Reflects risk profile [½]
Uncertainty should be verifiable [½]
Parameters should be identified and justified [½]
Complete [½]
Appropriate parameters [½]
Can be validated [½]
Rigorous and self-consistent [½]
Sufficiently detailed to deal adequately with key risk areas and capture homogeneous classes of business without being excessively complex [1]
Be capable of being run with changed parameters for sensitivity testing [1]
Use a sufficient number of simulations [½]
Have a robust software platform

Question 20

Outline the factors which should be considered when setting class groupings for the stochastic model

Answer 20

 class groups used elsewhere in the business, eg for reserving: – this avoids confusion when discussing inputs / outputs / results – the inputs received may be on a pre-existing structure so need to consider the practicality of splitting or aggregating
– reinsurance programmes usually apply to specific parts of the book only, so it’s usually sensible to model these splits as a minimum
 size of classes: – too many classes may lead to high parameter error and make model maintenance burdensome
– too few classes may render the model inadequate to help inform business decisions
 similarity of claim behaviour: – correlations with other claims, economy, etc – volatility of results within the proposed class
 purpose of model; if the model is to be used: – in setting targets for remuneration, then we must consider who is underwriting the different classes
– to compare plans to risk appetite, then results would need to be available at this level
 the sophistication of the model may restrict class groupings 
regulatory requirements

Question 21

Who are the key stakeholders the capital modelling team must engage with?

Answer 21

 Board / management – successful engagement with other business areas is likely to depend on first successfully engaging with the Board
 underwriting / pricing teams – without input from these teams, it’s unlikely the outputs will reflect the business being written
 reinsurance team: – reinsurance will probably materially impact the capital needed – reinsurance purchasing is often a key model use
 reserving / claims teams – likely to provide all the reserving parameters, and to have knowledge of cashflow timings for assessing liquidity risk
 investment team – the model can be used to understand the effect of different business mixes on capital requirements
 the risk team: – often involved in model validation – have a good understanding of key / emerging risks so can be useful in identifying gaps in the model
 IT team – buy-in from this team should enable the purchasing of appropriate software (and hardware) for the model
 regulators – often require companies to undergo stochastic modelling, hence sensible to clarify what the regulator expects in detail

Question 22

Describe three ways in which diversification effects can be allowed for in a capital model for a general insurance company.

Answer 22

1. Copulas (Stochastic allowance): [½]
   Copula is a mathematical relationship between individual distributions of random variables and the joint distribution [½]
   Simple correlation factors give rise to symmetric dependency structures [½]
   Some risks correlation vary in more complex ways (e.g. greater dependence in tail than around the mean) [½]
   Copula allows greater flexibility when modelling multiple dependencies than single correlation factor [½]
   Example of commonly used copula in insurance is Gumbel copula (½ mark given for this or any other relevant example with extra ½ mark available for formula) [1]
2. Deterministic allowance: [½]
   Where risks assessed in deterministic or semi stochastic method, apply standard methodology for summing variances of distributions (extra ½ mark available for formula) [1]
   Apply correlation matrix to extend method to two or more risks [½]
   Assume we can combine capital amounts in the same way as standard deviations of distributions [½]
   Where capital amounts are at extreme percentiles / tail of skewed distributions, this may not be mathematically correct [½]
3. Implicit correlations: [½]
   E.g. natural catastrophe event giving significant tail dependency for different classes [½]
   By measuring overall correlation, can validate whether this is consistent with explicit correlation assumptions being made and assess extent of implicit dependencies [½]
   Example of implicit correlation is driver correlation [½]
4. Linking assumptions: [½]
   If two assumptions in capital model explicitly linked through formulae already an implicit correlation between them [½]
   E.g. claims inflation assumption expressed as a margin above price inflation [½]
5. Explicit correlations: [½]
   For some assumptions, it may be appropriate to apply an explicit correlation factor (or a correlation matrix for multiple parameters)

Question 23

Why diversification is allowed for in capital models

Answer 23

Diversification effects arise because the various risks from a company’s operations are not perfectly correlated.
It is therefore unlikely that all segments of an insurer’s portfolio will perform adversely at any one time.
Hence, the capital required for the company as a whole will be less than the sum of the capital requirements for each separate risk / portfolio segment.

Question 24

Describe ways of assessing the stochastic model on a quantitative basis

Answer 24

1. Sensitivity testing
   • This is where parameters are changed by a small amount to test the impact on capital [1]
   • …This is a way of assessing which parameters in the model need more care when parameterising and what is driving the capital result [½]
   • …More detailed reviews are likely to take place of those parameters identified as being as sensitive [½]
2. Stress testing
   • This is where a single parameter is stressed materially to test the impact on capital in isolation [1]
   • …These changes are more extreme parameter changes than sensitivity testing. [½]
3. Scenario testing
   • This is where multiple parameters are changed to test their impact [1]
   • … Useful for considering combined effect of a number of a number of risks and cumulative effect of several different mitigating actions occurring at the same time[½]
   • …The company may independently parameterise a scenario and compare this to model output [½]
   • …This would be done to test if model scenarios are coming out at a similar return period to expert views [½]
4. Reverse stress testing
   • This would be experts coming up with a view of what would cause the business to cease to be viable and seeing if this is reflected by the model [1]
5. Backtesting
   • This involves comparing historic results to model outputs [1]
   • …This is done to check the model is sufficiently reflecting the real world [½]
   • …If there are 10 years of data and one is showing up as being a 1-in-100 result in the model then it is likely that the model parameterisation is not fully reflecting the real world unless there has been a material change recently [½]
6. Adding and removing dependencies
   • This would be done to test the importance of any dependencies within the model and to test if any material dependencies may have been missed out of the model [1]
7. Benchmarking
   • Comparing model outputs to benchmarks, e.g. industry results, other similar companies, other capital measures (e.g. statutory standard formulas) [1]
   Marks available for other sensible suggestions

Question 25

Describe two different methods that could be used to model market risk.

Answer 25

1. Stress testing [½]
   A firm using a simple stress test approach might undertake the following types of tests:
    A rise in interest rates of W% leading to reduced assets values and changed value of discounted liabilities (if the model discounts the liabilities) [½]
    An X % fall in equity prices [½]
    Currencies depreciating against sterling by Y% [½]
    A fall in property values by Z% [½]
    A change in the spread of corporate bonds/yields [½]
    In each case the degree of severity of the test will reflect the chosen confidence level
   [½]
    When carrying out stress testing, it is important to consider the relationships between risks [½]
   Appropriate when:
    Stress tests may be appropriate for insurers with standard investment portfolios [½]
    ..or where the insurer doesn’t have material exposure to market risk [½]
    If capital model being used is deterministic it may not be possible to use an ESG [½]
    Insurer may not have the capacity, expertise or money for an ESG [½]
    We may also use stress tests to provide a sense check on the output of a more complicated market risk model, such as Economic Scenario Generator [½]
    Any other suitable arguments
2. Use of an Economic Scenario Generator (ESG) [½]
    An ESG is a model that generates values for economic variables (such as inflation, gilt yields and equity returns) [½]
    ESGs are often viewed as superior to stress tests as they use common drivers of market risk, such as inflation [½]
    An ESG defines the forms the variables may take and the relationships between them
   [½]
    ESGs can be very complex so it is important that the user understands the inputs and ensures that the ESG has been calibrated to reflect the purpose [½]
    The ESG will give a joint probability distribution of outcomes for the economic variables [½]
   For example
   o equity returns, yield curve shifts, credit spread shifts, credit defaults (and so on) and a point is chosen from the distribution that reflects the desired confidence level [½]
    The point will have been generated by a particular scenario
   Appropriate when:
    An ESG may be appropriate if the insurer has a complex investment portfolio [½]
    or that wants to more accurately model the relationship between its insurance policies and the economy [½]
    or that wants to use the model to support its investment strategy [½]
    Market risk is material to the insurer [½]
    Often viewed as preferable / superior to stress tests as more complete [½]
    Any other suitable arguments

Question 26

How to perform actual versus expected exercise for capital modelling - for a Lloyd’s syndicate

Answer 26

 Obtain the results for the previous financial year, split by major business unit.
 Investigate what led to the results by discussing with business experts.  Extract the full distribution of results projected by the previous year’s capital model for each major business unit.
 Compare the financial results to the distributions to work out the return period of the observed results.
 Consider whether the return periods seem reasonable, given the results of the investigation and knowledge about what has happened in the year.
 If the return periods don’t seem reasonable then analyse what has led to this result, eg: – incorrect parameterisation of the model – a missing dependency – key variables not being modelled as stochastic – unmodelled event
 Lloyd’s business is modelled on an underwriting year basis.
 Lloyd’s requires each syndicate to carry out a profit and loss attribution exercise.

Question 27

Describe different ways of allowing for facultative reinsurance in a capital model, commenting on when they may be appropriate.

Answer 27

Explicitly model facultative reinsurance contracts … … may be practical if there a small number of material programmes. Model losses net of facultative reinsurance …
… could apply a simple proportional adjustment if facultative arrangements are not material. Use a net-to-gross ratio approach …
… if facultative arrangements are material but there are too many to model explicitly.

Question 28

Sources of profits and losses for general insurance company

Answer 28

 performance of unearned / new business different to business plan  inherent uncertainty in business performance  whether or not a catastrophe event happens …  … and any following demand surge
 change in strategy during year  planned activities not working out as expected  change in availability / cost of reinsurance compared to expectations 
legislation change
 position in underwriting cycle different to expected  expenses being different to expected …  … eg project cost different to budget  unforeseen change in any regulatory charges / levies  change in propensity to claim  costs of acquiring business different from expected
 deterioration or improvement in earned reserves
 change in reserving / booking philosophy  performance of assets different to expectations
 change in economic conditions  change in rules on assets that can be held / used for capital requirements
 cashflows different to expectations …  … causing liquidity constraints meaning assets sold at less advantageous times
 change in consumer behaviour influencing company to invest differently to plan, eg ESG concerns
 operational event happening …  … eg regulatory fine  default by reinsurer or counterparty

Question 29

Why does a GI decide to move from prudent to best estimate basis in its stochastic capital model

Answer 29

 To ensure that its reserve estimates are consistent with the other parameters in its capital model.
 To make any margins over best estimate clearer in the model.
 To provide a better indication of the percentile that reserves are being held at.
 Due to a regulatory requirement or they may be applying to have their model approved for capital setting.
 May have made a similar change to its reserving basis and the change avoids the need for different reserve estimates.
 To ensure consistency across the business.  May be easier to understand and communicate.
 To match published accounts if they need to be on a best estimate basis.
 It may be viewed as best practice.  To support better decision making.  To help embed the capital model in its business.  To enable the model to be used for other purposes.
 To reduce the amount of capital required for reserving, freeing it up to be used elsewhere.

Question 30

Suggest, with reasons, which parameters within the capital model may change following the change in basis from prudent to best estimate

Answer 30

 Reserve estimates gross and net of reinsurance …  … as they will be different on the new basis …  … either on an individual claim basis or in aggregate.  Gross reserve volatility …  … as the potential downside risk will change.
 Reinsurance parameters … – … including parameters used to model the reinsurers’ share of the claims volatility / variability …
– … claims may hit reinsurance programmes later than previously assumed …
– … the specific reinsurers that they are expecting to recover from may change …
– … may model the reinsurance programme explicitly or by applying factors to gross data …
– … if a broad-brush approach is used, any notional reinsurance panel will need to be updated.
 Any operational risk losses linked to the reserves.  The asset mix may change to match the revised cashflows …  … or due to the increase in free assets.  Claims emergence patterns …  … eg may have assumed claims happen earlier with strong inflation.

Question 31

Explain what inwards reinstatement premiums are and outline the various considerations when estimating them.

Answer 31

Inwards reinstatement premiums are the premiums for the restoration of the reinsurance cover to its full amount after a loss occurrence by the cedant. These are premiums payable to the reinsurer so are a cash inflow component of the reinsurer’s technical provisions and should be recorded and tracked separately. From an estimation perspective, they can be calculated explicitly at a policy level in relation to specific claims which trigger reinstatement premiums or at an aggregate level using chain ladder-based methods.
The circumstances under which reinstatement premiums are payable are specific to individual contracts and vary with contract terms, making aggregate methods more difficult to apply and may make actuarial projections unreliable if terms for reinstating reinsurance have changed over time (eg an increase in free reinstatements in a soft market), or comparisons to historical years cannot be made (eg catastrophe years compared to non-catastrophe years).
As with all premium estimation in early development, involvement of underwriters will be important to assess the income for individual portfolios. In particular, where reinstatement of coverage is in relation to catastrophe coverage post-event, underwriters will be involved in providing estimates of both the claims cost payable as well as any additional reinstatement premium receivable.

Question 32

Data items needed for modelling underwriting risk

Answer 32

1. unearned premiums at the date of the capital model
2. planned new business premium to be written over the period covered by the model
   3.planned loss ratios
3. planned expense ratios.
   All of the above split by LOB
4. historical claim frequencies and severities …
   … split between attritional claims, large losses and catastrophes … … and split by class of business
5. past inflation rates with which to revalue claims data
6. terms of existing reinsurance contracts pertaining to unearned business … … and planned future reinsurance programmes …
   … from which to calculate related ceded / expected ceded premiums … … including reinstatement premiums where applicable … … and expected recoveries
   views of the firm’s reinsurance department and brokers relating to the likelihood of reinsurance disputes …
   … and possible future changes in reinsurance rates

Question 33

Data items needed for modelling market risk

Answer 33

1. the current value of assets
2. the current mix of assets, eg by type, term and currency
3. past and current: – exchange rates, inflation rates, interest rates.
4. the current mix of liabilities, eg by term and currency past and current equity returns
5. yields on corporate and government bonds, split by duration and territory
6. credit ratings of bond counterparties, to assess default risk

Question 34

Data items needed for counterparty default risk

Answer 34

1. the reinsured share of unpaid claims, split by reinsurer
2. the reinsurance program (current and planned)
3. credit ratings for reinsurers
4. views of the firm’s reinsurance department and brokers, eg on possible losses in the event of default.
5. transitional probabilities for reinsurer downgrade
6. historical reinsurer failures
7. historical large losses
8. collateral held by the insurer, eg letters of credit
9. past non-recoveries due to reinsurance disputes
10. dependency between individual reinsurers / intermediaries defaulting
11. non-reinsurance credit exposures, eg broker balances

Question 35

Data items needed for liquidity risk

Answer 35

1. premium payment profiles, ie timings and amounts
2. claims payment profiles, ie sizes, frequencies and settlement patterns
3. expense payment profiles
4. data from specialist catastrophe modelling firms (both past loss data and data on potential catastrophe losses).
5. payment profiles for cashflow items such as: –
   reinsurance recoveries,
   reinsurance premiums payable, commissions,
   brokerage,
   investment income tax,
   dividends
6. details of any run-off business in the book.